Our civilization is, and always has been, object based, tactile, much more concerned with space than with time. The main reason would seem to be that we inherit our science and mathematics from the Greeks and, for historic and perhaps also temperamental reasons, they hankered after the stability and permanence which, for most of their era, they did not possess (note 1). The Greeks excelled above all in two areas where change is not immediately apparent or was deliberately eliminated : namely astronomy and geometry. Archimedes formulated the basic laws of statics and hydrostatics but the world had to wait nearly another two thousand years before Galileo and Kepler gave us the laws of motion. This preoccupation with solid matter and with changelessness is by no means a universal attitude : Buddhism, for example, has been described as “essentially a long meditation on impermanence” while Taoism positively exults in the ebb and flow of natural processes and counsels us, if we want to achieve happiness, to ‘abandon ourselves to the flow’.
Even when movement did make its belated appearance in ‘classical’ (i.e. Renaissance to mid 19th century) physics the early scientists dealt primarily with ‘extended bodies’, ‘inertial systems’, ‘ideal’ gases, and viewed the whole of Nature as subject to unchanging mathematical laws laid down by the Creator. When thermodynamics in the nineteenth century gave physics the notion of ‘entropy’ there was general consternation since it seemed to show that the whole marvellous machine was running down and that the universe would ‘in time’ become uninhabitable as all temperatures became uniform. Then came Einstein and Relativity and the world of science was never the same again (note 2).
The difficulty that so many people, even some physicists, have in dealing with four dimensions instead of three only demonstrates the materialistic bias of our whole civilization. Obviously, if we are dealing with relatively persistent and unchanging entities such as rocks or lumps of metal, we can afford to neglect the time dimension since such substances remain the same, or very nearly the same, from one day to the next, often from one century to another. But if we are talking about events, this is quite another matter.
Suppose a staccato event such as a pistol shot or a sudden flash of lightning. To locate this event spatially for the benefit of someone who was not present, it is sufficient to specify three, and no more than three, distances from a fixed point, say the corner of the room for the pistol shot. These three directions do not need to be at right angles to each other but in general this is the most convenient way of proceeding : an imaginary rectangle, extendable in all directions, with one corner baptised the ‘origin’ gives us a coordinate system. Alternatively, we can imagine a perfect sphere, make its centre the origin and precisely identify any spot by giving its distance from the centre and two angles. Latitude and longitude suffice to locate Waterloo if we mean the village in Belgium (or what is left of it), but this is not much use if we are referring to the battle. Human history is much more concerned with what happened than where such and such an event took place — what does it matter where Napoleon was when he decided to invade Russia?
The time dimension is, in reality, more fundamental than the spatial one, as Pearse correctly observed. One can (just about) imagine a world without extendable bodies, but not a world where nothing happens — one would not call it a world. All subjective events, wishes, fancies and so forth, though technically speaking localized ‘in our head’, have nothing to do with space : this is precisely why dreams and fantasies are attractive — they liberate us from the tyranny of spatial boundaries. This is a rather important point : it shows how the ‘time dimension’ is relatively independent of the spatial one, is dislocated from it, as it were, at least in our consciousness, if not in reality.

‘Time’ has in common parlance two very different meanings which are frequently confused : it sometimes means Succession (before and after) and sometimes Duration (how long?). Of these two meanings, there can be no doubt that the first, succession, is the more important since the only way we can evaluate duration meaningfully is by measuring the interval between two prominent events, the first and last in a chain of events. On the other hand, succession has no connection to duration : event B succeeds event A whether the interim is scarcely perceptible or centuries long. A person’s ‘life’ spans the inerval between a first event, the moment of birth (or sometimes the moment of conception) and a last event, the moment of death. Today, the ‘times’ of these two events can be specified with great precision and there can be no doubt about which of the two events comes before the other and that they really are the first and the last (of this particular sequence anyway). The extent of a lifetime or other interval between two successive events is always measured by referring it to some repeated event or cycle which we have reason to believe is regular, for example the periodic reappearance of the sun (so many days), or its return to the same spot as judged by the shadow cast on a stone (so many years). Otherwise, we have man-made devices on the same principle, swinging pendulums, vibrating atoms and so on. One could in principle measure a time interval with tolerable precision by recording one’s own heartbeats. In all such cases we have (1) a first and last event in a specific event chain, and (2) a (finite) number of events taking place in an adjacent event chain, or, in the case of heart beats, ‘within’ the very event chain we are measuring.
The Axioms of Ultimate Event Theory make this even more decisive. In a causally connected event chain — for the moment we assume that it is possible to recognize such a chain — there are always single events which we can take as ‘first’ and ‘last’. Every macroscopic event is made up of a finite number of ultimate events (Axiom of Finitude) and every ultimate event is precisely localized (Axiom of Locality). Moreover, in much the same way as we can, or could, measure a life-span in terms of heartbeats, we can measure the duration of any connected event chain by the number of (actual or possible) intermediate events. This number will be large but will not be infinite (Axiom of Finitude). Of course, in practice there may be serious difficulties in deciding whether such and such macroscopic events are causally connected or not, i.e. belong to the same chain, and the number of intermediary ultimate events will not, with our current technology at any rate, be ascertainable. But in principle this could be done. Such an event chain would be entirely determined both as to its constituent ultimate events and their number. (More will be said about this in a subsequent post.) We know athat, because of Relativity, there will be serious problems about relating this particular event chain to all the other event chains going on ‘at the same time’ but if we consider only a particular connected chain, and other chains occurring in its immediate vicinity, these problems do not arise.
Four, and seemingly no more than four, specifications are required to localize an event exactly. However, this does not mean that the four ‘dimensions’ enter the arena ‘on the same footing’ : manifestly they do not. The three spatial dimensions are inextricably intertwined and how we label them, i.e. which we call length, breadth, depth, x, y or z is obviously neither here nor there — provided we keep to the same labels we have assigned them to a particular case. I conceive of ‘space’ as being ‘continuous’ in the sense of there not being any obvious breaks or barriers between specific spots which can receive ultimate events, even though (by the Axiom of Locality combined with the Axiom of Finitude) there is not an ‘infinite’ number of possible locations for events between any two given spots. The three spatial dimenions -dimensions are thus (1) arbitrarily labelled with respect to the three different directions; (2) are at right angles to each other (in the normal coordinate representation); and (3) are continuous in that they ‘run into each other’ without any apparent breaks. But none of this is true of the time dimension (which renders all this talk about the fourth dimension being compared to ‘adding a third dimension to a flat surface’ completely vacuous). Why is this not true? Because the time dimension has only one possible direction and this direction is (I believe) imposed on us — the so-called Arrow of Time. Secondly, the time dimension does not ‘run into’ the three spatial dimensions but is very much out on its own, which is precisely why it was possible for so long to neglect it. Thirdly and most important of all, the time dimension is not continuous.
Suppose a set of objects in a particular neighbourhood at a particular moment, the contents of this room for example. A moment later, I see the same set of objects to all intents and purposes as they were before — though I know there have been some slight changes at an invisible level. I cannot conceive for the life of me how this room can get from what it is at one moment to what it is at another, later moment, except by disappearing and reappearing. Strangely enough, few Western thinkers have addressed this problem since nearly all of them assume that it is ‘natural’ for things to keep on existing from one moment to the next and, moreover, to make the transition without any kind of an interim. Descartes is about the only Western philosopher I know who was worried by the question, and he resolved it, to his own satisfaction at least, by invoking the perpetual intervention of God who, at each and every moment, prevented the entire universe from disappearing without trace by recreating it anew — the so-called ‘Theory of Continuous Creation’ (Note 3).
Now, I believe that the movement from present to future is discontinuous, that “Being is shot through with nothingess” as Heidegger put it in a memorable phrase. Not only that, I believe that we have a certain instinctive awareness of this breakage in ‘the flow of time’. For Newton and countless others, ‘time’ is imaged as a stream, a fluid at any rate that ‘flows’ in a particular direction — an idea that goes back to Heraclitus. The classic Indian Buddhist simile is quite other : it is that of a lamp flashing on and off repeatedy (note 4) . I find this simile much more plausible, and indeed, I have never felt at ease with the whole concept of ‘continuity’, which is not a physical but a mathematical concept. We now know that all transfers of energy are not continuous, as they were once thought to be, but are subject to quantum laws (come in chunks). Fluids appear to be continuous but in reality they are made up of molecules which we can even ‘see’, if only via an electron microscope. The last bastions of the continuous are ‘space’ and ‘time’ and, even here, some physicists are already suggesting that the ‘fabric of Space-Time’ might be ‘grainy’, as they put it. S.H.

Notes : (1) : During Plato’s lifetime Athens lost a long drawn out war with Sparta and was decimated by a plague. It is hardly surprising that Plato, and other men like him at the time, recoiled with horror from the human spectacle, taking refuge in a transcendent reality.

(2) Paradoxically, the man who did more than anyone else to bring time to the centre of the stage, ended up by dispensing with it completely. During his last years, Einstein apparently came to the conclusion that everything takes place “in an eternal present”. He seems to have been serious about this, since he mentions this idea in a letter of condolence he wrote after hearing about the death of his undergraduate friend, Besso.

(3) Bergson “The world the mathematician deals with is a world that dies and is reborn at every instant, the world which Descartes was thinking about when he spoke of continuous creation” (Bergson, Creative Evolution p. 23-4). Stcherbatsky, who quotes this statement, remarks that “His [Descartes’] idea is quite Buddhistic and the Sanscrit translation sounds like a quotation from an Indian text” (Stcherbatsky, Buddhist Logic Vol. 1 Footnote p. 108). The Buddhist theory is rather one of ‘Instantaneous Being’ since there is no Creator : the appearance and disappearance of dharma is a purely mechanical process, a sort of cosmic karma.

(4) “The Buddhist theory of Universal Momentariness (ksanikatva’), converting the universe into a kind of cinema, meaintains that there is no other cause of destruction than origination, entities disappear as soon as they appear, the moment when the jar is broken a stroke of a hammer does noit differ in this respect from all preceding moments, since every moment a new or ‘other’ jar appears, constant desrtruction or renovation is inherent in every existence which is really a compact series of ever new moments.” Stcherbatsky, Buddhist Logic Vol. 2 Page 93 Footnote)